Renyi Entropy for Local Quenches in 2D CFTs from Numerical Conformal Blocks

TL;DR

This paper investigates the time evolution of Renyi entanglement entropy in 2D large central charge CFTs after local quenches, revealing a universal logarithmic growth and a phase transition at a specific primary operator dimension.

Contribution

It provides a numerical analysis of conformal blocks and uncovers a new universal formula for entropy growth when the primary operator dimension exceeds a critical value.

Findings

Logarithmic growth of entanglement entropy with a computed coefficient.

Discovery of a phase transition at operator dimension c/32 affecting conformal block behavior.

Confirmation of analytical results using the HHLL approximation.

Abstract

We study the time evolution of Renyi entanglement entropy for locally excited states in two dimensional large central charge CFTs. It generically shows a logarithmical growth and we compute the coefficient of $\log t$ term. Our analysis covers the entire parameter regions with respect to the replica number $n$ and the conformal dimension $h_O$ of the primary operator which creates the excitation. We numerically analyse relevant vacuum conformal blocks by using Zamolodchikov's recursion relation. We find that the behavior of the conformal blocks in two dimensional CFTs with a central charge $c$, drastically changes when the dimensions of external primary states reach the value $c/32$. In particular, when $h_O\geq c/32$ and $n\geq 2$, we find a new universal formula $\Delta S^{(n)}_A\simeq \frac{nc}{24(n-1)}\log t$. Our numerical results also confirm existing analytical results using the HHLL approximation.